Pirate missions are offered in Corvus ala old "guard our Wormhole" missions.

Anti-pirate missions are offered in non-corvus grey space stations.

Both missons reward player kills:
100,000 credits
Combat XP
Light Weapons XP *Very important
Heavy Weapons XP *Very important

The XP is based on the formula:
100+(Opponent's Duel Score) - (Your Duel Score)
If your Duel Score exceeds your opponent then your recieve 100 XP.

The Pirate mission also rewards NPC Convoy Kills:
10,000 Credits
50 Combat, Light, & Heavy XP for Transports
100 Combat, Light, & Heavy XP for Fighters

When you take either mission your are automatically grouped with other players taking the mission.

Like Escort and anti escort?

Opposing factions would have missions vs each other.

Faction A has an escort mission
Faction B has a raid mission set to destroy the escorted convoy